U.S. Republican presidential candidate Donald Trump has taunted Fox News and anchor woman Megyn Kelly in particular, a day after pulling out of a televised debate with party rivals this week over anger at the network.

"I refuse to call Megyn Kelly a bimbo, because that would not be politically correct," Trump said on Twitter. "Instead I will only call her a lightweight reporter!"

On Tuesday, Trump said he would not participate in the debate, scheduled for Thursday in Des Moines, Iowa, expressing irritation at Fox for allowing Kelly to moderate after her questioning angered him in a debate last year.

His withdrawal means the last televised debate before Iowa's pivotal Feb. 1 nominating contest will not have the party's front-runner in a close state race. Iowa's caucuses are the first nominating contest to choose the Republican presidential nominee for the Nov. 8 election.

Trump has been feuding with Fox News since the network put on the first debate in August, when Kelly asked Trump about his treatment of women, prompting a stream of insults from the candidate and complaints of not being treated fairly.

His Republican rivals have criticized him for dropping out while his closest rival in Iowa, U.S. Senator Ted Cruz of Texas, challenged him to a one-on-one debate. In a Twitter post on Wednesday, Cruz likened Trump's withdrawal to a comical retreat from a "Monty Python" movie.

Former Arkansas Governor Mike Huckabee on Fox News program, "Fox and Friends" on Wednesday called the affair "a lot of drama" that most Iowa caucus-goers would likely tune out.

In a separate interview on Fox, retired neurosurgeon Ben Carson said it was time to "stop worrying about personalities and start worrying about solutions."

Trump campaign manager Corey Lewandowski told several television programs on Wednesday that Trump was not afraid to debate his rivals or take reporters' questions. He added that Trump would be happy to debate Cruz if the contest, which includes 12 Republicans vying for the nomination, narrows.

"If it comes down to a two-person race, Donald Trump would be happy to debate him," he told ABC's "Good Morning America" program.

Fox News, in a statement late Tuesday, said it would not "give in to terrorizations toward any of our employees," but left the door open to Trump attending the debate, co-hosted by Google.

Trump tweeted: "The statement put out yesterday by @FoxNews was a disgrace to good broadcasting and journalism. Who would ever say something so nasty & dumb."

Trump has said he will instead hold an event for veterans.

"At the end of the day, Mr. Trump is going to have the last laugh," Lewandowski told MSNBC.

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